Learning-based state estimation in distribution systems with limited real-time measurements

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The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time, indicating the existence of multiple states that result in identical values for the available measurements. Certain existing approaches utilize historical data to infer the relationship between real-time available measurements and the state. Other learning-based methods aim to estimate the measurements acquired with a delay, generating pseudo-measurements. Our paper presents a methodology that utilizes the outcome of an underdetermined state estimator of an unobservable network state estimator to exploit information on the joint probability distribution between real-time available measurements and delayed ones to generate new physics-informed interpretable features. Through numerical simulations conducted on two realistic distribution grids of different size with insufficient real-time measurements, the proposed procedure showcases superior performance compared to existing state forecasting approaches and those relying on inferred pseudo-measurements.